It is estimated that one could expect \({\cal O}(10^{10})\) 
of \(B_{c}\)  mesons per year at the LHC [1]}.
Along with the running of the LHC, more and more \(B_{c}\) 
decay modes will be observed.
Anticipating the experimental developments, many studies
(see Table.) have been devoted to the bottom
conserving and charm changing decay modes \(B_{c}\)  \({\rightarrow }\) 
\(BP\) , \(BV\) , including estimates undertaken within various
quark models assisted by confining potential [2]}, [3]}, [4]}, [5]}, [6]},
with potential models based on the Bethe-Salpeter equation
[7]}, [8]},
with BSW or ISGW models [9]}, [10]},
with QCD sum rules [1]},
with heavy quark spin symmetry [12]},
with QCD factorization at the leading order [13]},
but without perturbative QCD (pQCD) approach.
In this paper, we study the \(B_{c}\)  \({\rightarrow }\)  \(BP\) , \(BV\) 
decays with the pQCD approach [14]} to fill in this
gap and provide a ready reference to the existing and
forthcoming experiments.
